## Calculus: Early Transcendentals 8th Edition

$dm=5p^{4}q^{3}dp+3p^{5}q^{2}dq$
Given: $m=p^{5}q^{3}$ The differential form can be evaluated as follows: $dw=\dfrac{\partial w}{\partial x} dx + \dfrac{\partial w}{\partial y} dy$ We need to find the partial derivatives w.r.t. $p$ and $q$ as follows: $dm= \dfrac{\partial m}{\partial p}dp+\dfrac{\partial m}{\partial q}dq$ Here, we get $\dfrac{\partial m}{\partial p}dp=(5) p^{4}q^{3}dp$ and $\dfrac{\partial m}{\partial q}dq=(3) p^{5}q^{2}dq$ Hence, we have $dm=5p^{4}q^{3}dp+3p^{5}q^{2}dq$